Filtering and Control of High Speed Motor Current in a Flywheel Energy Storage System ·  · 2013-04-10Filtering and Control of High Speed Motor Current in a Flywheel Energy Storage

Barbara H. Kenny and Walter SantiagoGlenn Research Center, Cleveland, Ohio

Filtering and Control of High Speed MotorCurrent in a Flywheel Energy Storage System

NASA/TM—2004-213343

October 2004

AIAA–2004–5627

https://ntrs.nasa.gov/search.jsp?R=20040171483 2018-06-08T22:29:28+00:00Z

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Barbara H. Kenny and Walter SantiagoGlenn Research Center, Cleveland, Ohio

Filtering and Control of High Speed MotorCurrent in a Flywheel Energy Storage System

NASA/TM—2004-213343

October 2004

National Aeronautics andSpace Administration

Glenn Research Center

Prepared for theSecond International Energy Conversion Engineering Conferencesponsored by the American Institute of Aeronautics and AstronauticsProvidence, Rhode Island, August 16–19, 2004

AIAA–2004–5627

Available from

NASA Center for Aerospace Information7121 Standard DriveHanover, MD 21076

National Technical Information Service5285 Port Royal RoadSpringfield, VA 22100

Available electronically at http://gltrs.grc.nasa.gov

Filtering and Control of High Speed Motor Current in aFlywheel Energy Storage System

The NASA Glenn Research Center has been developing technology to enable the use ofhigh speed flywheel energy storage units in future spacecraft for the last several years. Anintegral part of the flywheel unit is the three phase motor/generator that is used to accelerateand decelerate the flywheel. The motor/generator voltage is supplied from a pulse widthmodulated (PWM) inverter operating from a fixed DC voltage supply. The motor current isregulated through a closed loop current control that commands the necessary voltage fromthe inverter to achieve the desired current. The current regulation loop is the innermostcontrol loop of the overall flywheel system and, as a result, must be fast and accurate overthe entire operating speed range (20,000 RPM to 60,000 RPM) of the flywheel. The voltageapplied to the motor is a high frequency PWM version of the DC bus voltage that results inthe commanded fundamental value plus higher order harmonics. Most of the harmoniccontent is at the switching frequency and above. The higher order harmonics cause a rapidchange in voltage to be applied to the motor that can result in large voltage stresses acrossthe motor windings. In addition, the high frequency content in the motor causes sensor noisein the magnetic bearings that leads to disturbances for the bearing control. To alleviatethese problems, a filter is used to present a more sinusoidal voltage to the motor/generator.However, the filter adds additional dynamics and phase lag to the motor system that caninterfere with the performance of the current regulator. This paper will discuss the tuningmethodology and results for the motor/generator current regulator and the impact of thefilter on the control. Results at speeds up to 50,000 rpm are presented.

Nomenclatureiqs

r q-axis current (torque producing) in the rotor reference frame, ampsids

r d-axis current in the rotor reference frame, ampsV r*

qds Commanded motor phase voltage vector in rotor reference frame, voltsV s*

qds Commanded motor phase voltage vector in stator reference frame, voltsis qds Motor phase current vector in the stationary reference frame, amps

ir qds Motor phase current vector in the rotor reference frame, amps

qr^

Estimated rotor angle, degrees

wr^

Estimated rotor speed, rad/sectem Motor/generator torque, N-mlaf Motor/generator back EMF constant, volt-secL Inductance, henriesC Capacitance, faradsR Resistance, ohmsKi Integrator gain constantKp Proportional gain constants LaPlace operatorVdc DC bus voltage, voltsf Fundamental frequency, Hz

Barbara H. Kenny and Walter SantiagoNational Aeronautics and Space Administration

Glenn Research CenterCleveland, Ohio 44135

NASA/TM—2004-213343 1

I. IntroductionLYWHEEL energy storage units are an attractive alternative to traditional batteries in space applications thatrequire large numbers of charge / discharge cycles, wide operating temperature ranges, or peaking power for

short periods. In addition, multiple flywheels can be used on a satellite to provide both energy storage and attitudecontrol, thus combining two subsystems into one. Flywheels are composed of multiple subsystems including thehigh inertia flywheel rotor, the motor/generator, the magnetic bearings and the auxiliary bearings as shown in Fig. 1.The NASA Glenn Research Center has been developing advanced technologies for these subsystems over the lastseveral years and has demonstrated energy storage at 60,000 rpm with one unit and combined single axis attitudecontrol and energy storage using two units [1,2].

One important area of research is thedevelopment of the motor/generatorcontrols. Algorithms have been developedto control the motor/generator such thatthe flywheel can store energy in chargemode and supply energy to loads indischarge mode while regulating the DCbus voltage [1]. Additional algorithmshave been developed to combine theattitude control and energy storagefunctions of two separate flywheel units[2,3]. The innermost loop of the flywheelcontrol for all of the algorithms is acurrent loop that is based on the fieldorientation control technique in whichcurrent is directly proportional to motortorque [4,5]. A block diagram of the fieldorientation control of the flywheelmotor/generator is shown in Fig. 2.

In the field orientation technique, amathematical transformation is performed on the current variables such that all of the control is done in a referenceframe that is synchronous with the rotor. This allows the control quantities to become DC values and thus thebandwidth of the current regulator is not affected by the fundamental frequency of the machine. In addition, if therotor reference frame d-axis current, ids

r , is regulated to zero, the machine torque becomes linearly proportional to therotor reference frame q-axis current, iqs

r as shown in Eq. (1) where laf is the back EMF constant of the machine. Thusthe machine torque response is directly proportional to the current response.

tem = 32

laf iqsr (1)

To perform the reference frame transformation properly, continuous rotor angular position feedback informationis necessary. In typical industrial implementations, this information is provided by an additional sensor such as anencoder or a resolver. For the flywheelapplication, due to the high operatingspeed required, there is no position orspeed sensor on the shaft. A “sensorless”position and speed estimation algorithmprovides the necessary information byusing the measured motor phase currentvalues and the commanded motor voltage,Vqds

s* , values to continuously estimate rotorposition and speed. This is described indetail in reference [6].

As the innermost loop of the entireflywheel control system, the algorithmshown in Fig. 2 must deliver a fast andaccurate torque response over the entire

F

Figure 1. Flywheel Unit and Components

Figure 2. Motor Control Block Diagram

NASA/TM—2004-213343 2

operating speed range of the motor/generator. The key component to accomplishing this is the current regulatorbecause the current is directly proportional to the torque as shown in Eq. (1). This paper discusses the currentregulator performance with respect to the effect of the AC filter, proper tuning, and the operating speed with resultspresented for 20 kRPM and 50 kRPM operation (60,000 RPM was not demonstrated for this paper but has beendocumented previously [7,8]).

II. AC Filter

The AC filter is necessary in this application for a number of reasons. First of all, it reduces the dv/dt stress thatthe motor winding sees due to the high frequency (65 kHz) switching. Switching at a high frequency is necessary to

create a high fidelity 1 kHz fundamental frequency atthe full speed value of 60,000 RPM. Secondly, thefilter reduces the current ripple in the motor. Thecurrent ripple is significant without the filter becausethe machine inductance is relatively low. With thefilter, this ripple is approximately 1 amp, peak topeak. It also reduces the common mode noise in boththe motor and the magnetic bearings due to theparasitic capacitive coupling between the windingsand the motor housing. The eddy current sensorsused to sense the rotor shaft position for the magneticbearings are particularly sensitive to high frequencynoise. Further detailed discussion of the design andbenefits of the AC filter can be found in [9].

The AC filter itself consists of two cascadedfilters: a 65 kHz “trap” filter tuned to reduce theharmonics at the switching frequency, and a fourpole, two stage low pass filter tuned with a 10 kHzcorner frequency. The circuit diagram of one phase

of the three phase filter is shown in Fig. 3. VA is the voltage at the inverter terminal, Va is the voltage at the motorterminal and n is the filter neutral. The motor neutral is not connected but the filter neutral is connected to themidpoint of the DC bus capacitor on the DC side of the inverter. The filter has the component values given in Table1.

III. Synchronous Frame Current RegulatorThe synchronous frame current regulator [10] shown in the block diagram in Fig. 2 consists of two PI

controllers, each one acting on an axis of current, as shown in Figs. 4 and 5. The outputs of the current regulatorsresult in a rotor reference frame voltage command that is converted to a phase voltage (line-neutral) command in thestationary reference frame. The conversion is accomplished using the estimated rotor angle, qr

^ , as shown in Fig. 2.

The commanded phase voltage is synthesized from the DC voltage by the highfrequency pulse width modulation (PWM) switching of the inverter.

From a controls perspective, the simplest model of the motor is an R-Lcircuit in the rotor reference frame as described by Eqs. (2) and (3).

di r qs

dt =

1Lq

ËÊ

¯ˆ V r

qs - Rsir qs (2)

di r ds

dt =

1Ld

ËÊ

¯ˆ V r

ds - Rsir ds (3)

Using LaPlace variables and rearranging terms results in expressions for thetransfer functions as shown in Eqs. (4) and (5) .

i r qs

V r qs

=

1

Lq

s + Lq

Rs

(4)

Figure 3. Filter Circuit Diagram

Filter Component Name ValueL1 15 mHL2 7 mHLt 76.12 mHC1 16.89 mFC2 36.19 mFCt .077 mFR .5 W

Table 1. Filter Component Values

Figure 4. q-Axis SynchronousFrame Current Regulator

Figure 5. d-Axis SynchronousFrame Current Regulator

NASA/TM—2004-213343 3

i r ds

V r ds

=

1

Ld

s + Ld

Rs

(5)

The motor model can now be combinedwith the current regulator model into oneblock diagram so that the initial tuning of theregulator can be found as shown in Figs. (6)and (7). The PI current regulator has beenrewritten in a form to show the zero of thecontroller and the inverter is modeled with atransfer function of 1. Note that with thesimple R-L model of the motor in the rotorreference frame, there is no coupling betweenthe d- and q- axes.

The simple inverter model with a transferfunction equal to 1 is reasonably accurate for the fundamental frequencies as long as the magnitude of thecommanded voltage does not exceed a maximum value that is dependent on the DC bus voltage magnitude and themodulation technique. The magnitude of the commanded voltage is given in Eq. (6) and is the same in both therotating and stationary reference frames. The modulation technique used in the flywheel system is known as spacevector modulation. For this modulation technique, the maximum commanded voltage magnitude that allows theinverter to remain in the linear region of control (transfer function equal to 1) is given in Eq. (7) [11].

|V r*qds| = (Vr*

qs)2 + (Vr*

ds)2 = |V s*

qds| = (Vs*qs)

2 + (Vs*ds)

2 (6)

|V r*qds| ≤ Vmax =

Vdc

3(7)

Based on Figs. 6 and 7, the transfer function of the q- and d-axis currents are given in (8) and (9), respectively.

i rqs

ir*qs

= KpË

ʯˆ

s + Ki

Kp

LqsËÊ

¯ˆ

s + Rs

Lq + KpË

ʯˆ

s + Ki

Kp

(8)

i rds

ir*ds

= KpË

ʯˆ

s + Ki

Kp

LdsËÊ

¯ˆ

s + Rs

Ld + KpË

ʯˆ

s + Ki

Kp

(9)

For the purpose of tuning the current regulator, Ls, the average of the d- and q-axis inductances, is used. With this inmind, if the gains in Eqs. (8) and (9) are set according to Eq. (10), then the transfer functions reduce to the valuesshown in Eqs. (11) and (12).

Rs

Ls =

Ki

Kp (10)

i rqs

ir*qs

= Kp

Ls

1

ËÊ

¯ˆ

s + Kp

Ls

(11)

i rds

ir*ds

= Kp

Ls

1

ËÊ

¯ˆ

s + Kp

Ls

(12)

The bandwidth of the response can then be set according to Eq. (13) with the selection of Kp which sets the polesof Eqs. (11) and (12) to the desired location. The bandwidth in this equation corresponds to the response of themotor torque and is theoretically independent of the fundamental frequency and operating speed of the machine.

Figure 6. q-Axis Controller and Motor Block Diagram

Figure 7. d-Axis Controller and Motor Block Diagram

NASA/TM—2004-213343 4

fbw= Kp

2pLs Hz (13)

Generally, the phase resistance and inductance of the motor are used in Eqs. (10) through (13) to calculate thecurrent regulator gains and bandwidth. Even if perfect pole-zero cancellation is not achieved in Eqs. (8) and (9),either the response is adequate for a particular application, or the gains can be tuned heuristically starting from thecalculated values until the desired response is achieved. However, if the filter introduces a large impedance into thecircuit, the response can be significantly different than expected. The initial tuning can be improved by modifyingthe inductance and resistance values used in Eqs. (10) through (13) to include the effect of the filter impedance.

The filter impedance can be calculated using a Thevenin equivalent impedance approach and the circuit diagramof Fig. 3. The Thevenin equivalent voltage is basically the fundamental voltage from the inverter with significantlyreduced 65 kHz switching content and harmonics. It has very little phase lag or magnitude change within theoperating frequency range (0-1000 Hz) as discussed in [9]. The Thevenin equivalent impedance of the filter shownin Fig. 3 is a 6th order equation that is given in the Appendix. At the frequencies of interest, however, it ispredominantly inductance, and this is most easily seen by actually measuring the impedance of the circuit using animpedance analyzer and then calculating the equivalent inductance and resistance. Three possible circuitconfigurations were measured: the motor only, the motor with the two stage filter of Fig. 3 but without the L-C trapportion, and the motor with the entire filter of Fig. 3. The results are given in Table 2.

Motor OnlyMotor plus filter without

trapMotor plus filter with trap

(Fig. 3)Frequency(Hz)

Req (mW) Leq (mH) Req (mW) Leq (mH) Req (mW) Leq (mH)100 33 39 66 64 84 140200 36 38 68 63 87 139300 38 37 71 62 90 138400 41 37 74 62 94 138500 44 36 78 62 99 137600 47 36 82 62 104 137700 50 35 87 62 109 137800 54 35 93 62 116 137900 57 34 99 62 122 1371000 60 34 106 62 130 137

Average 46 36 82 62 104 138

Table 2. Circuit Resistance and Inductance Values Calculated from Impedance Measurements.

Based on the measured resistance and inductance, two sets of gains can be calculated for various bandwidthsusing (10) and (13) as shown in Table 3.

Motor Only ParametersMotor plus two stage filter (no

L-C trap)Motor plus two stage &

trap filter (Fig. 3)BandwidthKp Ki Kp Ki Kp Ki

1 kHz .2 544 .39 515 .87 6541.5 kHz .3 820 .58 773 1.3 9762 kHz .4 1088 .78 1030 1.73 1308

Table 3. Current Regulator Gains for Various Bandwidths.

IV. Experimental Results

For all of the experimental results, the two stage with L-C trap filter (Fig. 3) was used between the output of theinverter and the motor as shown in Fig. 2. However, the first two sets of results presented herein use currentregulator gains based on the motor parameters alone, without consideration of the effect of the filter. Theperformance consequences of not including the filter impedance in calculating the gains can then be seen. The restof the results use the gains based on the entire circuit impedance measurement: motor plus two stage and L-C trapfilter (the last two columns of Table 3). All of the results use the gains calculated for a 2 kHz bandwidth.

Two speeds within the operating range of the flywheel system, 20,000 RPM and 50,000 RPM, were tested. Ingeneral, either set of gains worked well at 20,000 RPM. The response was fast and there was very little overshoot or

NASA/TM—2004-213343 5

oscillation. In contrast, operation at 50,000 RPM wasmore challenging and required modifications of thecontroller to achieve the desired performance. To bestdemonstrate the performance improvements resultingfrom the control modifications, the subsequent datapresented is at 50,000 RPM. The control modificationsalso improve performance at low speeds but theimprovement is more evident at higher speeds and thusthe high speed data is presented herein.

Figures 8 through 12‡ show 20,000 RPM operationusing the motor alone gain parameters. Figure 8 showsthe phase current response to a step change command inmotor q-axis current from 1.5 amps to 20 amps.Figures 9 and 11 show the motor q-axis current (andestimated torque) and the motor speed. The motoraccelerates at a constant rate after the step change,indicating a constant motor torque as shown on Fig. 11.

Figure 9. Motor Commanded (red) and Actual (blue)q-axis Current and Equivalent Torque at 20 kRPM.

Figure 10. Expanded Scale of Motor q-axis CurrentResponse at 20 kRPM.

Figure 11. Motor Speed for Step Change inCommanded Current at Time t=0 at 20 kRPM.

Figure 12. Expanded Scale of Motor d-axis CurrentResponse at 20 kRPM.

‡ In all of the plots in this paper, the red trace is the commanded value and the blue trace is the measured value.

Figure 8: Motor Phase Current Response to StepChange in q-Axis Current Command at 20 kRPM.

NASA/TM—2004-213343 6

Figures 10 and 12 show an expanded time scaleversion of the q- and d-axis current response. It can beseen that the q-axis current rises to the commandedlevel with a response time on the order of 2 kHz butwith some overshoot. The d-axis current exhibits adisturbance when the q-axis step change occurs. Thisis due to coupling between the d- and q-axes that is notaccounted for in the simple R-L model of the motorand will be discussed in Section V.

Figures 13 through 17 give the results at 50,000RPM, again using the gains based only on the motorparameters. This corresponds to an 833 Hzfundamental frequency of current and voltage. It canbe seen that at this speed there is significant oscillationas the current reaches the commanded value. Figure15 shows that the overshoot of the q-axis currentreaches almost 150% of the commanded value and theoscillation takes over 20 msec. to dampen out. The

Figure 14. Motor Commanded and Actual q-axisCurrent and Equivalent Torque at 50 kRPM.

Figure 15. Expanded Scale of Motor q-axis CurrentResponse at 50 kRPM.

Figure 16. Motor Speed for Step Change inCommanded Current at Time t=0 at 50 kRPM.

Figure 17. Expanded Scale of Motor d-axis CurrentResponse at 50 kRPM.

Figure 13. Motor Phase Current Response to StepChange in q-Axis Current Command at 50 kRPM.

NASA/TM—2004-213343 7

current regulator performance using the motorparameters only gains is not acceptable at high speedsand may even become unstable for larger disturbances.In contrast, Figs. 18 through 22 show the currentregulator performance at 50,000 RPM using the gainscalculated with the total measured impedance (motorplus the two stage filter with L-C trap, Fig. 3, and a 2kHz bandwidth from Table 3). The overshoot is stillpresent but it is reduced in magnitude and there is noperiod of extended oscillation. The q-axis currentsettles to the commanded value in less than 5 msec.and the rise time is very fast, achieving the desired 2kHz bandwidth. However, the d-axis current stillexhibits a large transient during the step change in theq-axis command. This transient can be reduced byaugmenting the current regulator to compensate for thecross coupling between the q- and d-axes that is notrepresented in the simple models of Eqs. (4) and (5)

Figure 19. Motor Commanded and Actual q-axisCurrent and Equivalent Torque at 50 kRPM withFilter Gains.

Figure 20. Expanded Motor q-axis Current Responseat 50 kRPM with Filter Gains.

Figure 21. Motor Speed during transient at 50 kRPMwith Filter Gains.

Figure 22. Expanded Motor d-axis Current Responseat 50 kRPM with Filter Gains.

Figure 18. Motor Phase Current Response at 50kRPM, with Filter Gains.

NASA/TM—2004-213343 8

Figs. 6 and 7. The cross-coupling causes the d-axis current to exhibit a response to a q-axis change and the q-axiscurrent to exhibit a response to a d-axis change. For a perfectly decoupled system, a change in the q-axis currentshould cause no change in the d-axis.

V. Back EMF Decoupling

The current response can be improved by designing the current regulator using the complete motor modelinstead of the simple R-L model previously given in Eqs. (4) and (5). The complete state equations are given in (14)and (15) for the permanent magnet machine modeled in the rotor reference frame [5].

di rqs

dt =

1Lq

ËÊ

¯ˆ V r

qs - Rsir

qs - Ldwrir

ds - wrlaf (14)

di rds

dt =

1Ld

ËÊ

¯ˆ V r

ds - Rsir

ds + Lqwrir

qs (15)

In addition to the resistance and inductance terms of the simple R-L model, there is now a cross-coupling term ineach equation that is dependent on the inductance, the speed and the current in the other axis. In addition, there isthe back EMF term in the q-axis equation, wrlaf, that represents the voltage produced by the rotor magnets as theyrotate through the stator windings.

The effect of the cross-coupling can be removed by adding terms to the current regulator that anticipate andapproximately cancel the coupling terms using a technique known as back EMF decoupling [5]. If the motorparameters are known exactly, the result of back EMF decoupling is to reduce the motor state equations to thesimple R-L model given earlier in Eqs. (4) and (5). This is shown in (16) and (17) where the ^ symbol indicates theestimated value of the parameter. The block diagram of the total system, current regulator and motor model, isshown in Fig. 23. The right half of the block diagram is the motor model and the left half is the current regulatorwith back EMF decoupling. The gain values, Kp and Ki, remain the same as given in Table 2.

di rqs

dt =

1Lq

ËÊ

¯ˆ V r

qs - Rsir

qs - Ldwrir

ds - wrlaf + 1

Lq^

ËÊ

¯ˆ Ld

^ wri

rds + wrlaf

^ ≈ 1Lq

ËÊ

¯ˆ V r

qs - Rsir

qs (16)

di rds

dt =

1Ld

ËÊ

¯ˆ V r

ds - Rsir

ds + Lqwrir

qs - 1

Ld^

ËÊ

¯ˆ Lq

^ wri

rqs ≈

1Ld

ËÊ

¯ˆ V r

ds - Rsir

ds (17)

Figure 23. Back EMF Current Regulator and PM Motor Modeled in the Rotor Reference Frame.

NASA/TM—2004-213343 9

The results using the controller with the back EMFdecoupling added are shown in Figs. 24 through 28.The flywheel speed is 50,000 rpm and the gains are thesame as for the results shown in Figs. 18 through 22.The decoupling current regulator reduces the d-axisovershoot as can be seen by comparing Fig. 28 to Fig.22. In addition, the q-axis current peak is also reducedas shown in Fig. 26 versus Fig. 20. However, Fig. 24shows a greater phase current overshoot than in Fig. 18in spite of the improvements seen in the d- and q-axes.In the ideal case, an improvement in the q- and d-axisresponse should lead to a corresponding improvementin the phase current response.

The most likely explanation for this discrepancy isthat there is an error between the actual and estimatedrotor angle, qr

^ , that is used in the reference frame

transformations necessary for the field orientation

Figure 25. Motor Commanded and Actual q-axisCurrent and Equivalent Torque at 50 kRPM withFilter Gains and Back EMF Decoupling.

Figure 26. Expanded Motor q-axis Current Responseat 50 kRPM with Filter Gains and Back EMFDecoupling.

Figure 27. Motor Speed during transient at 50 kRPMwith Filter Gains and Back EMF Decoupling.

Figure 28. Expanded Motor d-axis Current Responseat 50 kRPM with Filter Gains and Back EMFDecoupling.

Figure 24. Motor Phase Current Response at 50kRPM, with Filter Gains and Back EMF Decoupling.

NASA/TM—2004-213343 10

control technique. The estimated rotor angle is based primarily on the assumption that the commanded voltage, V s*qds,

is equal to the actual motor phase voltage [6]. However, the filter adds additional impedance between the inverterand the motor as already described. This impedance has an associated phase lag that adds to the controller samplingand processing time lag. The total phase shift will appear directly as an error in the estimation of the rotor positionangle, qr

^ . The result of using an inaccurate rotor angle is to introduce additional coupling between the d- and q-axis

in the torque response of the machine and also to deviate from the most efficient (measured as maximum torque peramp) operating point. Identifying and quantifying the impact of rotor angle estimation errors is an area of futurework.

VI. DC Bus Voltage LimitAs discussed in Section III, the motor control is based on the assumption that the transfer function between the

commanded voltage and the output fundamental voltage from the inverter is equal to 1. This is true as long as thecommanded voltage is less than the maximum value given in Eq. (7). In the flywheel system with a DC bus voltageof 125 volts, the maximum peak value is 72 volts, line to neutral. This peak value ultimately limits the speed of themachine because as the speed increases, so does the required motor phase voltage. This can be seen from the motorstate equations given in Eqs. (14) and (15) rearranged to see the necessary voltage for various operating conditionsas shown in Eqs. (18) and (19). Equation (20) describes the peak phase voltage magnitude.

V rqs = Rsi

rqs + Ldwri

rds + wrlaf + Lq

di rqs

dt (18)

V rds = Rsi

rds - Lqwri

rqs + Ld

di rds

dt (19)

| |V r qds = (Vr

qs)2 + (Vr

ds)2 (20)

For steady state operation (constant speed), thederivative terms in (18) and (19) become zero. Thecommanded d-axis current is zero and if the rotorangle used in the reference frame transformation iscorrect, the actual d-axis current will also be zero andthus the ids

r terms will be equal to zero in the equations.The voltage equations then reduce to Eqs. (21) and(22).

V rqs = Rsi

rqs + wrlaf (21)

V rds = - Lqwri

rqs (22)

It can be seen from Eqs. (21) and (22) that atsteady state, the magnitude of the voltage applied tothe machine will be dominated by the back EMFvoltage (the wrlaf term). This is because the voltagedrop across the motor resistance in Eq. (21) and thevoltage drop across the inductance in Eq. (22) aresmall compared to the back EMF voltage, particularlyat high speeds. During a step change in the currentcommand, however, the voltage magnitude willincrease sharply due to the non-zero value of thederivative term in Eq. (18). After the step, during theacceleration of the machine, the voltage magnitudewill continue to be higher than in steady state becausethe current, iqs

r , increases to provide the torquenecessary for acceleration.

The voltage magnitude during the steady state, the step change transient, and the acceleration phases can be seenin Figs. 29 and 30 for 20,000 RPM and 50,000 RPM operation, respectively. Both plots are for a 2 kHz bandwidthsystem using back EMF decoupling and the gains given in Table 3 (with the filter of Fig. 3). In addition, Fig. 30corresponds to the same test run as reported in Figs. 24 to 28. It can be seen from the figures that the voltage spike

Figure 29. Commanded Phase Voltage During StepChange in Current Command at 20 kRPM.

Figure 30. Commanded Phase Voltage During StepChange in Current Command at 50 kRPM.

NASA/TM—2004-213343 11

due to the step change in the current command at time t=0 is within the maximum available voltage for 20,000 RPMoperation but exceeds it for approximately a millisecond for 50,000 RPM operation. During this time, the inverterprovides the maximum voltage possible but cannot provide the commanded value. However, the current is able toeventually reach the correct operating point even though the commanded voltage is not available for the firstmillisecond of the transient.

It can also be seen from the figures that for the 20,000 RPM operation case, the voltage magnitude behaves asdescribed above: close to the back EMF voltage at steady state (t < 0) and slightly higher than the back EMF voltageduring acceleration (t > 0). For the 50,000 RPM case, the voltage magnitude is approximately equal to the backEMF voltage in steady state but it clearly decreases during acceleration. This would seem to contradict theexplanation given above, however, that derivation is based on the assumption that the reference frametransformations are accomplished correctly through accurate knowledge of the rotor angle. In the presentimplementation of the controller, a phase lag between the commanded voltage and the voltage applied to the motorwould cause a rotor angle estimate that lags the actual angle and results in a non-zero (negative) ids

r term. A negativeids

r will reduce the voltage magnitude as can be seen from Eqs. (18), (19) and (20). This is the most likely cause ofthe voltage magnitude reduction observed in Fig. 30. As stated previously, work is presently underway to improvethe rotor angle estimate and quantify any errors, particularly at high speeds, and it is expected that a more accurateestimate will resolve the discrepancies between the expected and measured behavior. It is interesting to note,however, that the controller still continues to provide an excellent overall response in spite of the suspected rotorangle estimation error.

Returning to the problem of the commanded voltage exceeding the available voltage, one possible solution is tolimit the value of the derivative term in Eq. (18) by limiting the rate of change of the commanded current. If a 2kHz response is desired, it is not necessary to change the current command in a step fashion but rather limit it to aramp function that represents a command change within 2 kHz. Figures 31 through 36 show the results for a 2 kHzbandwidth response, tuned with the gains of Table 3, and a 60 kA/sec ramp for the commanded value of current, ir*

qs,

as it transitions from 1.5 to 20 amps. This means that the derivative term in Eq. (18), di r

qs

dt , will be approximately

equal to 60 kA/sec. Figure 31 shows the peak voltage command to be significantly less than the case without theramp command and now well below the maximum available voltage. In addition, the current response is improved.There is less overshoot on the d-axis current (Fig. 36) and the q-axis current shown in Fig. 34 still has a 2 kHzresponse with an approximate settling time of 2 msec (a shorter time than the results without the ramp limit).

VII. ConclusionsThis paper has presented a discussion of the tuning techniques used for the current regulator of the NASA GRC

flywheel system. The flywheel system electronics incorporate an AC filter between the inverter and themotor/generator to reduce the dv/dt stress on the motor and to improve the magnetic bearing control. The AC filteradds additional dynamics to the system that must be considered when tuning the current regulator in order to achievethe desired performance at high speeds. The current regulator was initially tuned without consideration of the ACfilter and the results were satisfactory at low speeds. However, as the speed increased, the response to a step changein current command was found to be more and more oscillatory. The oscillations were eliminated and a fastresponse was achieved when the current regulator gains were changed to include the impedance of the AC filter. Theresponse with the adjusted gains was improved further by augmenting the current regulator with a back EMFdecoupling portion and limiting the rate of change of the commanded current. A step change in current command isnot a realistic command trajectory and limiting the current command to a ramp achieves the desired bandwidth withless overshoot and settling time. The ramped command also reduces the voltage command overshoot during thetransient thus ensuring that the commanded voltage can be achieved at all times.

A few discrepancies were noted that were most likely caused by an error in the estimated rotor position. Addingback EMF decoupling to the current regulator did not reduce the transient overshoot in the actual phase current eventhough it was reduced in the q- and d-axes. For a perfect transformation, the phase current transient would have alsobeen reduced. Additionally, the commanded voltage was lower than the back EMF voltage at high speeds duringacceleration. Again, with perfect transformation using the exact rotor position angle, the commanded voltage isexpected to be higher than the back EMF voltage during acceleration. Quantifying and correcting the suspected rotorposition estimation error is the next step for the improvement of the flywheel motor/generator control.

However, the overall goal of achieving current regulation with a 2 kHz bandwidth for speeds up to 50,000 RPMwas achieved and documented. This type of current response enables the high performance torque control necessaryfor the flywheel operation at all speeds.

NASA/TM—2004-213343 12

Figure 31. Commanded Phase Voltage During StepChange in Current Command with 60 kA/sec RateLimit.

Figure 32. Motor Phase Current with 60 kA/sec RateLimit at 50,000 RPM.

Figure 33. Motor q-axis Current with 60 kA/sec RateLimit.

Figure 34. Magnified View of Motor q-axis Currentwith 60 kA/sec Rate Limit.

Figure 35. Motor Speed During Step Change inCurrent Command with 60 kA/sec Rate Limit.

Figure 36. Magnified View of Motor d-axis Currentwith 60 kA/sec Rate Limit..

NASA/TM—2004-213343 13

AppendixThe Thevenin equivalent circuit was calculated for the filter shown in Fig. 3. The results are given below where

Vthev,numerator is the Thevenin voltage numerator, Vthev,denominator is the Thevenin voltage denominator, Zthev,numerator is theThevenin impedance numerator, and Zthev,denominator is the Thevenin impedance demoninator.

Vthev,numerator = s3R2C2LtCt + s2LtCt + sR2C2 + 1 (23)

Vthev,denominator = s6C1C2L1L2CtLt + s5L1C1R2C2LtCt + s4(C1C2L1L2 + L2C2LtCt + L1C2LtCt + L1C1LtCt) + s3(L1C1R2C2 + R2C2LtCt) + s2(LtCt + L2C2 + L1C2 + L1C1 + LtC2) + s(R2C2) + 1 (24)

Zthev,numerator = s6(C1C2CtL1L2LtR2) + s5(C1CtL1L2Lt) + s4(C2CtL1LtR2 + C2CtL2LtR2 + C1C2L2LtR2 + C1C2L1L2R2) + s3(CtL1Lt + CtL2Lt + C1L2Lt + C1L1L2) + s2(C2LtR2 +C2L1R2 + C2L2R2) + s(L1+L2+Lt) (25)

Zthev,denominator = s6(C1C2CtL1L2Lt) + s5(C1C2CtL1LtR2) + s4(C2CtL1Lt + C1C2L1L2 + C1CtL1Lt + C2CtL2Lt + C1C2L2Lt) +s3(C1C2LtR2 + C2CtLtR2 + C1C2L1R2) + s2(LtC2 + LtCt + C1Lt + C1L1 + C2L2 +C2L1) + sC2R2 + 1 (26)

For the filter without the L-C trap, the Thevenin values are as follows.

V thev,no L-C trap = sR2C2 + 1

s4(C1C2L1L2) + s3(L1C1R2C2) + s2(L2C2 + L1C2 + L1C1) + s(R2C2) + 1 (27)

Z thev,no L-C trap = s4(C2C1L1L2R2) + s3(C1L1L2) + s2(C2L1R2 + C2L2R2) + s(L1+L2)

s4(C1C2L1L2) + s3(C1C2L1R2) + s2(C1L1 + C2L2 +C2L1) + sC2R2 + 1 (28)

References1 Kenny, Barbara H.; Kascak, Peter E.; Jansen, Ralph; Dever, Timothy; “A Flywheel Energy Storage System Demonstration

for Space Applications.” NASA/TM—2003-212346, Proceedings of the International Electric Machines and Drives ConferenceMadison, Wisconsin, June 1-4, 2003.

2 Kenny, Barbara H., Kascak, Peter E., Jansen, Ralph, Dever, Timothy and Santiago, Walter, “Demonstration of Single AxisCombined Attitude Control and Energy Storage Using Two Flywheels,” NASA/TM—2004-212935, Proceedings of the 2004IEEE Aerospace Conference [CD ROM], Big Sky, Montana, March 6-13, 2004.

3 Kascak, Peter E., Jansen, Ralph, Kenny, Barbara H. and Dever, Timothy, “Demonstration of Single Axis Spacecraft AngleControl and DC Bus Regulation with Two Flywheel Energy Storage Units,” accepted for publication at the IEEE IndustryApplications Society (IAS) Annual Meeting, Seattle, Washington, October, 2004.

4 Kenny, Barbara H., Kascak, P., Hofmann, H., Mackin, M., Santiago, W., and Jansen, R., “Advanced Motor Control TestFacility for NASA GRC Flywheel Energy Storage System Technology Development Unit,” NASA/TM—2001-210986,Proceedings of the 2001 Intersociety Energy Conversion Engineering Conference [CD ROM], Savannah, GA, July 29- Aug. 2,2001.

5 Ramu, Krishnan, Permanent Magnet Synchronous and Brushless DC Motor Drives: Theory, Operation, Performance,Modeling, Simulation, Analysis and Design, Virginia Polytechnical Institute, Blacksburg, Va., 1999.

6 Kenny, Barbara H., and Kascak, P., “Sensorless Control of Permanent Magnet Machine for NASA Flywheel TechnologyDevelopment”, NASA/TM—2002-211726, Proceedings of the 2002 Intersociety Energy Conversion Engineering Conference[CD ROM], Washington, D.C., July 28- Aug. 2, 2002.

7 Kenny, Barbara H., Kascak, Peter E., Jansen, Ralph, Dever, Timothy and Santiago, Walter, “Control of a High SpeedFlywheel System for Energy Storage in Space Applications,” Pending NASA/TM (2004-XXXXXX) publication.

8 Kenny, Barbara H., “Motor Control of Two Flywheels Enabling Combined Attitude Control and Bus Regulation,”Conference Presentation, 2004 Space Power Workshop, Manhattan Beach, CA., April 19-22, 2004.

9 Santiago, Walter, “Inverter Output Filter Effect on PWM Motor Drives of a Flywheel Energy Storage System,” accepted forpublication at the 2nd International Energy Conversion Engineering Conference, Providence, RI., August 16-19, 2004.

10 Rowan, T. and R. Kerkman, “A New Synchronous Current Regulator and an Analysis of Current-Regulated PWMInverters,” IEEE Transactions on Industry Applications, Vol IA-22, No. 4, July/August 1986, pp. 678-690.

11 Holtz, Joachim, “Pulsewidth Modulation for Electronic Power Conversion,” Proceedings of the IEEE, Volume 82, No. 8,August, 1994, pp. 1194-1214.

NASA/TM—2004-213343 14

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E–14811

WBS–22–319–20–M1

20

Filtering and Control of High Speed Motor Current in a Flywheel EnergyStorage System

Barbara H. Kenny and Walter Santiago

High speed motor control; Flywheel energy storage; Current regulation

Unclassified -UnlimitedSubject Categories: 44 and 20 Distribution: Nonstandard

Prepared for the Second International Energy Conversion Engineering Conference sponsored by the AmericanInstitute of Aeronautics and Astronautics, Providence, Rhode Island, August 16–19, 2004. Responsible person,Barbara H. Kenny, organization code 5450, 216–433–6289.

The NASA Glenn Research Center has been developing technology to enable the use of high speed flywheel energy storage unitsin future spacecraft for the last several years. An integral part of the flywheel unit is the three phase motor/generator that is used toaccelerate and decelerate the flywheel. The motor/generator voltage is supplied from a pulse width modulated (PWM) inverteroperating from a fixed DC voltage supply. The motor current is regulated through a closed loop current control that commands thenecessary voltage from the inverter to achieve the desired current. The current regulation loop is the innermost control loop of theoverall flywheel system and, as a result, must be fast and accurate over the entire operating speed range (20,000 to 60,000 rpm) ofthe flywheel. The voltage applied to the motor is a high frequency PWM version of the DC bus voltage that results in thecommanded fundamental value plus higher order harmonics. Most of the harmonic content is at the switching frequency andabove. The higher order harmonics cause a rapid change in voltage to be applied to the motor that can result in large voltagestresses across the motor windings. In addition, the high frequency content in the motor causes sensor noise in the magneticbearings that leads to disturbances for the bearing control. To alleviate these problems, a filter is used to present a more sinusoidalvoltage to the motor/generator. However, the filter adds additional dynamics and phase lag to the motor system that can interferewith the performance of the current regulator. This paper will discuss the tuning methodology and results for the motor/generatorcurrent regulator and the impact of the filter on the control. Results at speeds up to 50,000 rpm are presented.